The Study Of Eighth Grade Students’ Understanding And Mastery Of Mathematical Thought And Method

Mathematical thinking and methods play an important role in mathematical education activities.From the 1992 "Nine-year Compulsory Education Full-time Junior High School Mathematics Teaching Syllabus(Trial)",which included mathematical thinking and methods in the two-base objectives,to the "Compulsory Education Mathematics Curriculum Standard(2011edition)",which formally proposed the "four-base" teaching objectives.The new "basic activity experience" and the change of "basic thinking" can be verified.Mathematical thought and method is the embodiment of the essence of mathematical knowledge.Understanding and mastering it can better cultivate and develop students’ creative thinking.Among them,the idea of equation is the most widely used in the middle school mathematics education activities of a kind of mathematical thinking method,it has realized the leap from arithmetic to equation,promoted the development of algebra,has an important position in the middle school mathematics learning.At present,the research on equation thought mainly focuses on the infiltration of thought method,teaching strategy and application,while the research on the understanding and mastery of equation thought is less,so it is of great significance to study students’ understanding and mastery of equation thought.This study mainly investigated the 8th grade students’ understanding and mastery of equation ideas.Firstly,through the collection,arrangement and induction of relevant literature,the connotation of mathematical thinking and equation thinking is clarified.Combined with psychology,different degrees or levels of understanding and related studies,the researcher divided students’ understanding of equation ideas into three dimensions: connotation understanding,applied understanding and representational understanding,and then defined the behavior of each dimension.There are three levels of the mastery of equation thought,and the corresponding survey test papers ⅰ and ⅱ are compiled accordingly.Test paper ⅰ investigates the understanding of equation thought by grade 8 students,and test paper ⅱ investigates the mastery of equation thought by grade 8 students.SPSS21.0 data analysis software was used to analyze the current eighth-grade students’ understanding and mastery of equation ideas.At the same time,in order to further understand the problems existing in the understanding and mastery of equation ideas among grade 8 students,some grade 8 students and teachers were selected for interviews:Firstly,the interview outline of students and teachers was prepared according to relevant theoretical basis.Secondly,students at different levels and front-line teachers were selected to interview.Finally,the reasons for some problems existing in students’ understanding and mastery of equation ideas and corresponding teaching suggestions were obtained according to the interview results.Through the investigation and research on the understanding and mastery of equation thought of eighth grade students,the following main conclusions are drawn:(1)Students in grade 8 generally have a good understanding and mastery of the idea of equations.(2)The understanding of equation thought: in general,the eighth-grade students have a better understanding of equation thought,in which students perform best in the representation understanding dimension,followed by the application understanding dimension,and finally in the connotation understanding dimension.(3)The mastery of equation thought: On the whole,grade 8 students have a good command of equation thought,with the best performance in level 1,followed by Level 2 and level 3.(4)There is no gender difference in the understanding and mastery of equation ideas among grade 8 students,and the overall performance is similar.Main problems existing in the understanding and mastering of equation ideas:(1)The eighth grade students have a one-sided understanding of the connotation of equation thought.They can only grasp some elements of the connotation of equation thought,but cannot organically combine all elements to form a complete understanding of equation thought.(2)The main reasons for the problems in the dimension of understanding the connotation of equation ideas: a.In actual mathematics learning,there is no topic to discuss mathematical ideas and methods.When encountering such uncommon problems,students will feel difficult and do not know how to express the connotation of equation ideas;b.In daily teaching,teachers often apply the idea of equation to solve certain kinds of problems,but do not elaborate on the connotation of the idea of equation.(3)Weak basic knowledge,poor memory of basic mathematical formulas and properties.(4)Operational problems: problems in solving equations/equations.(5)Weak perception of the superiority of equation ideas in solving problems: a.In algebra problems,I still use the arithmetic I am familiar with in primary school to solve problems;B.In geometry problems,we are more accustomed to using equal quantity substitution to solve problems,resulting in problems in the complex substitution process.(6)Consciously use equation ideas to solve problems,but the ability to extract information is weak.For problems with complex and implicit equal quantity relations,the correct equation or system of equations cannot be established.